I'm not too familiar with medical history but I've done some reading and took a class on the Black Death. I'm sure there are others that would be more qualified on this topic.

Your second assumption is correct, the predator animals and the rats became infected with plague and died, so having a cat or dog would be useless to stop the spread of plague. Actually, the death of the rats is said to be one of the main causes as to why the disease would spread to humans. The rats would die and then the fleas would need to find another host, making its way to people.

The sudden death of a huge amount of rats would actually warn people during the 3rd outbreak in the 19th century in China of plague. The death of the rats was noted by many people and recorded in some poems that talked about the plague. This actually became a point of debate among historians since the death of the rats was noted by so many people in China during the 19th century, but not during the Middle Ages and the European outbreak. Many people were unsure if the diseases were the same since no records from the Middle Ages mention the sudden death of hundreds of rats, even though the symptoms were the same. However, tests have been done since then and have proved that the diseases were almost identical, or at least related if I remember correctly. Some historians hypothesize that the disease during the Middle Ages may have been spread differently. However, this is getting beyond my knowledge and I can't mention any specific examples.

Sources: Great Britain, Colonial Reports, Miscellaneous, Hong Kong, “Memorandum on the Treatment of Patients in their own Homes and in Local Hospitals,” 1903.

Benedict, Carol. Bubonic Plague in Nineteenth-Century China. Stanford: Stanford University Press, 1996.

Lehfeldt, Elizabeth A. The Black Death (Boston: Houghton Mifflin, 2005)

Naphy, William and Andrew Spicer, Plague: Black Death and Pestilence in Europe (The Mill: Tempus Press, 2004 [2000]).